One reply that is important stated this "There is better overall aircraft performance than you may suspect due to the real OAT is colder than the assumed temperature input for the engines. The engines would produce the same thrust if operated at the assumed temperature, but the wing is flying in the denser air at the actual OAT".
That may have been the case with the old paper charts, but it doesn't appear to be the case with the Boeing OPT software that I currently use. I have just performed a sample calculation which produced an ATM of 34C with OAT of 30C, then repeated the calculation with OAT of 0C. The N1 was over 5% lower at the lower OAT. So I'm thinking the OPT "knows" about the improved performance at the lower OAT. Can anyone verify this? Of course, it may be that it is lowering the N1 to provide an equivalent thrust at the given OAT, and may not necessarily be considering improved lift.